Real Options Models of the Firm, Capacity Overhang, and the Cross Section of Stock Returns

• Author: KEVIN ARETZ,PETER F. POPE
• Date: 01 June 2018
• DOI: http://doi.org/10.1111/jofi.12617
• Published date: 01 June 2018

THE JOURNAL OF FINANCE •VOL. LXXIII, NO. 3 •JUNE 2018

Real Options Models of the Firm, Capacity

Overhang, and the Cross Section of

Stock Returns

KEVIN ARETZ and PETER F. POPE∗

ABSTRACT

We use a stochastic frontier model to obtain a stock-level estimate of the difference be-

tween a firm’s installed production capacity and its optimal capacity. We show that

this “capacity overhang” estimate relates significantly negatively to the cross sec-

tion of stock returns, even when controlling for popular pricing factors. The negative

relation persists among small and large stocks, stocks with more or less reversible

investments, and in good and bad economic states. Capacity overhang helps explain

momentum and profitability anomalies, but not value and investment anomalies.

Our evidence supports real options models of the firm featuring valuable divestment

options.

RECENT STUDIES USE REAL OPTIONS THEORY to establish links between a firm’s

capacity-related decisions, systematic risk, and characteristics. Focusing on

a firm that owns both installed production capacity and costly-to-reverse

growth options, a common result in these studies is that the firm’s ex-

pected return depends on the difference between its installed capacity and the

level of capacity that maximizes firm value net of capacity installation costs

∗Kevin Aretz is at Alliance Manchester Business School. Peter Pope is at London School of

Economics and Bocconi University. We are indebted to two anonymous referees, two anonymous

Associate Editors, and the Managing Editor (Kenneth Singleton) for helpful and constructive sug-

gestions. We are also indebted to Axel Adam-M¨

uller, Christopher Anderson, Michael Brennan,

John Campbell, Robert Dittmar, Adlai Fisher, Luis Garcia-Feij´

oo, Massimo Guidolin, Dirk Hack-

barth, Andrew Karolyi, Holger Kraft, Peter Nyberg, Gil Sadka, Mark Shackleton, Mathijs Van

Dijk, Michela Verado, Rafal Wojakowski, Ania Zalewska, and seminar participants at the Uni-

versity of Bath, University of Bristol, University of Cambridge, University of Dauphine (Paris),

University of Exeter, University of Lille, Lisbon School of Economics and Management, London

School of Economics, Luxembourg School of Finance, University of Surrey, University of Trier, the

2012 INQUIRE Autumn Seminar in London, the 2013 London Quant Group Seminar in Oxford, the

2014 Arne Ryde Workshop in Financial Economics in Lund, the 2014 Old Mutual Global Investors

Quant Conference in Oxford, the 2015 Real Options Conference in Athens, and the 2015 Deutsche

Bank Annual Global Quantitative Strategy Conference in New York for insightful comments. We

have read the Journal of Finance’s disclosure policy and have no conflicts of interest to disclose.

This is an open access article under the terms of the Creative Commons Attribution-NonCom-

mercial License, which permits use, distribution and reproduction in any medium, provided the

original work is properly cited and is not used for commercial purposes.

DOI: 10.1111/jofi.12617

C2018 The Authors. The Journal of Finance published by Wiley Periodicals, Inc. on behalf of

American Finance Association

1363

1364 The Journal of Finance R

(“capacity overhang”).1,2There is disagreement, however, about the exact na-

ture of the expected return-capacity overhang relation. For example, assuming

highly irreversible but cheap-to-exercise growth options, Carlson, Fisher, and

Giammarino (2004), Zhang (2005), and Cooper (2006) predict a mostly posi-

tive relation, potentially explaining value and investment anomalies in stock

returns. Assuming more reversible growth options, Sagi and Seasholes (2007),

Guthrie (2011), and Hackbarth and Johnson (2015) predict a negative relation,

potentially explaining momentum and profitability anomalies. Combining low

investment reversibility with expensive-to-exercise growth options, Hackbarth

and Johnson (2015) show that the relation can also be U-shaped, potentially

explaining both groups of anomalies above.3

Given the strong theoretical foundations underlying the expected return-

capacity overhang relation, there is surprisingly little empirical research on

the shape of the relation and its implications for stock anomalies. The lack of

empirical research probably reflects the difficulty in estimating stock-level ca-

pacity overhang. We make an effort to close this gap in the literature. Weemploy

a stochastic frontier model to estimate stock-level capacity overhang. Using the

model’s estimates, we run portfolio sorts and Fama-Macbeth (FM) (1973) re-

gressions to study the shape of the stock return-capacity overhang relation.

We also run horse races between the capacity overhang estimate and value,

momentum, investment, and profitability variables, which allows us to study

whether capacity overhang helps explain these anomalies.

We start with a theoretical analysis of a version of Pindyck’s (1988) real

options model of a firm that allows for costly investment reversibility. We show

that this standard demand-based real options model is able to produce the

different expected return-capacity overhang relations established in earlier

work. More importantly, we also gain insights that inform our empirical esti-

mation of capacity overhang from the model. The model considers a firm that

sells output at a stochastic price. The firm maximizes value by taking costless

production (i.e., capacity utilization) decisions and capacity adjustment (i.e.,

1Assuming that the cost of a capacity unit does not depend on installed capacity, we can intu-

itively think of the capacity level that maximizes net firm value (“optimal capacity”) as the initial

capacity chosen by a start-up firm with the same values for the state variable and the model pa-

rameters. Firms sometimes build up capacity in excess of this level because capacity installation

costs exceed the resale value of capacity, creating a wedge between the value of the state variable

at which the firm invests and the value at which it divests.

2We note that capacity overhang is related, but not identical to, “excess capacity,” which is

usually defined as the proportion of a firm’s installed capacity used in production. We focus on

capacity overhang because first, it is a more fundamental concept than excess capacity (i.e., capacity

overhang determines excess capacity, but not necessarily vice versa), and second, our stochastic

frontier model approach allows us to estimate capacity overhang, but not excess capacity.

3Value anomalies describe the tendency of value stocks to have higher returns

than growth stocks. Investment anomalies describe the tendency of noninvesting (or divesting)

stocks to have higher returns than investing stocks. Momentum anomalies describe the tendency of

high intermediate-term past return stocks (winners) to have higher returns than low intermediate-

term past return stocks (losers). Profitability anomalies describe the tendency of profitable stocks

to have higher returns than unprofitable stocks.

Capacity Overhang and Returns 1365

investment and divestment) decisions under fixed capacity purchase and sale

prices. In the absence of capacity adjustment options, the model produces a

positive expected return-capacity overhang relation. This occurs because a

firm with sufficiently high-capacity overhang produces below full capacity.

Thus, such a firm is able to increase (decrease) its capacity utilization rate as

the output price increases (decreases), which renders its profits more sensitive

to changes in the output price.

Endowing the firm with capacity adjustment options changes the expected

return-capacity overhang relation. Growth options enable an optimal-capacity

firm to invest and further increase profits as the output price rises, increasing

the firm’s expected return, while divestment options enable a high-capacity-

overhang firm to divest and mitigate falling profits as the output price drops,

lowering the firm’s expected return. Thus, when we introduce growth op-

tions, the expected return-capacity overhang relation can become U-shaped,

and when we introduce both growth and divestment options, the relation can

become negative.

In our empirical work, we employ a novel approach to estimating stock-level

capacity overhang, namely, a stochastic frontier model. The stochastic frontier

model decomposes installed production capacity into an optimal capacity term

and a capacity overhang term, identifying the two terms using different de-

terminants and appropriate distributional assumptions. The most important

distributional assumption is that capacity overhang cannot be negative. In our

main specification, we use a firm’s property, plant, and equipment (PPE) plus

intangible assets to proxy for installed production capacity. Informed by the

real options model, we specify optimal capacity as a function of sales, operat-

ing and nonoperating costs, volatility, systematic risk, and the risk-free rate

of return. We include industry fixed effects to capture unobservable optimal

capacity determinants (e.g., investment costs). Also informed by the real op-

tions model, we specify capacity overhang as a function of variables reflecting

past decreases in a firm’s demand. We estimate the model recursively, which

ensures that the capacity overhang estimate could have been computed in real

time. Validation tests suggest that the capacity overhang estimate captures

time-series and cross-sectional variation in stock-level investment behavior

and industry-level capacity utilization rates obtained from surveys.

We next form value-weighted portfolios sorted on estimated capacity

overhang to study the stock return-capacity overhang relation. Mean excess

returns decline almost monotonically over the portfolios, with a spread across

the extreme portfolios of –12.5% per annum (t-statistic: –4.20). Adjusting

for risk using the CAPM, Hou, Xue, and Zhang’s (2015)Q-theory model, or

Fama-French’s (2015) five-factor model, we find that the spread return attracts

a negative and strongly significant loading on the profitability factors in the

Q-theory and five-factor models, which helps explain the mean spread return.

In contrast, the spread return loads positively, although less significantly, on

all other factors in the models. Thus, the spread portfolio alphas do not differ

much from the spread portfolio mean excess return. Similarly, FM regressions

of single-stock returns on the capacity overhang estimate and the joint set